System of calculating.



Patented 1an. I6, |900.

A. HORVATH.

SYSTEM F CLCULATING.

(Appxiqtion med Feb. 11; 1899.) y

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Patented I an. I6, |900. A. HDRVATH. f

SYSTEM 0F cALcULATlNG.

(Application led Feb. 11, 1899.)

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No. l64|,.294. lmerma 1an. ls, |900. A. HoRvATH.

SYSTEM 0F CALCULATING.

(Application filed Feb. 1l, 1899.)

(No Mode.) I 3 Sheets-Sheet 3.

M55/7165565 In vm 94%. S. /Hwmcm UNITED STATES PATENT EEICE.

AErD HoEvTH, or EUDA-rEsrH, AUSTRIA-Ennemi?.

SYSTEM oF CALCULTING.

srEcIrIcA'rroN forming par@ of Letters Patent No. 641,294, datedJanuary' 1e, 1eoo.

Application filed February 11, 1899. Serial N. 705,260. (N0 mOdeL) Toall whom t may concern:

Beit known thatI, ARPD HORVTH, asubject of the Emperor ofAustria-Hungary, residing at Buda-Pesth, Austria-Hungary, have inventedcertain new and useful Improvements in Systems of Calculating, (forwhich I have applied for patents in England, dated December 24, 1898; inGermany, dated December 17, 1898; in Austria, dated December 23, 1898;in France, dated December 26, 1898; in Belgium, dated December 24, 1898;in Italy, dated December 22, 1898; in Switzerland, dated December 21,1898; in Sweden, dated December 23, 1898, and in Norway, dated December24, 1898,) of which the following is a specification.

This invention relates to a new or improved system of calculating, andcomprises a system of calculating rods or bars, by means of whichmultiplication and division may be speedily and almost mechanicallyeected. The manipulation of these calculating-bars is far simpler thanis the case with calculating-machines'as hitherto constructed and may bereadily mastered.

The invention is illustrated in the accompanying drawings, in which-Figure 1 shows the eleven bars constituting the system. Figs. 2 to 6illustrate various examples of the use of the said bars. Fig. 7represents a pattern which enables the figures required to be morereadily found. Fig. 8 is a plan view of the calculating-bars. Fig. 9 isa perspective view of the frame of a pattern. Fig. 10 ,is a perspectiveview of one cf the calculating-bars.

The bars may be made of wood, metal, or other suitable material in theform of long rectangular prisms. The system of bars consists of anindex-bar A and of ten or more calculating-bars B. One side of theindexbar A is divided into ten squares, as illustrated, the topmost ofwhich forms what is termed the head, while each of the remaining ninesquares is marked in order with one of the numerals 1 to 9, running fromtop to bottom. The calculating-bars B are divided into ten squares uponeach of their four sides. At the head of each side is marked one of thenumerals from O to 9, (see Figs. 7 and 8,) while in the remainingdivisions the product or the head figure and of the numerals of theseries l to 9 is marked. (See Fig. 1.) Each of the divisions or squaresis divided by means of Va diagonal line into two triangles, in which theunit of the product is arranged below the diagonal and the ten above it,Fig. 1. In addition to this the triangular spaces below the diagonal areor may be colored-red, for examplein order to facilitate the finding ofthe required iigures. are also marked, in addition to the head figure,to the right and left and above it, smaller iigures, indicating the headfigures of the remaining sides of the bar.

In order to effect any operation of multiplication, those bars areselected the head numbers of which correspond with one of the factors.These bars B are laid beside the indexbarA in the order of the igures ofthe factor, and the figures of the other factor are found upon theindex-bar. Upon a level with the figures so found the squares of thecalculating-bars form separate horizontal columns, which contain thewhole of the elements of the product sought. These elements are thenadded together in accordance with the value represented by theirposition in order to obtain the required product. This operation isillustrated in Fig. 2 by means of two simple examples. In the upperexample (three multiplied by six hundred and forty-seven) a numberconsisting of one figure is to be multiplied by a number containingseveral figures. The one-figure factor 3 is found upon the in- In thetopmost division there dex-bar, and the calculating-bars having the headiigures 6, 4, and 7, which constitute the number 647, are laid besidethe index-bar in the order named. In the horizontal columns which are ona level with the index figure 3 are to be found the numbers 18, 12, and21, forming elements of the required product. If these elements areadded together in a manner corresponding to the value of the position ofthe respective head figures in the number GeV-that is to say, the ten of21 to the unit of 12 and the ten of 12 to the unit of 18--the product1,941 is obtained.

The example illustrated in the lower portion of Fig. 2 represents theoperation of multiplying sixty-seven by six hundred and forty-seven, inwhich case the elements 36,

IOO

24, 42, 42, 28,and 49 are found in the horizontai columns opposite theindex-figures 6 and 7. The addition of these elements in a mannercorresponding to their place value is represented in Fig. 3, the figuresin question being replaced by identical letters provided with variousindices. The number having the lowest place value is designated by theletter d, which in the present case represents the unit and alwaysstands in the last or outermost colored triangle of the topmost orundermost row. The sum of the numbers designated by b, b2, and b3 givesthe tens; the sum of the numbers designated by c', c2, c3, and c4, thehundreds; the sum of the numbers designated by d', d2, and d3, thethousands, and the number designated by e, the ten-thousands. From thisfigure the rule may readily be deduced in accordance with which theelements must be added together-that is to say, the numbers which standin the oblique row formed by the diagonals belong one to the other, or,in other words,-have to be added together as if arranged in a verticalcolumn, and the place value of these rows increases from the right tothe left hand. This rule is of general application also in the casewhere the figures of the first factor do not constitute any connectedportion of the series 1, 2, 3, 4, 5, 6, 7, 8, 9- that is to say, whenthe horizontal columns of the elements do not stand directly one underthe other, but when other columns not connected therewith come betweenthem or when the figures in the factor form a connected butuniformly-falling series of numerals. In this latter case, however, thehorizontal columns of the elements must be first arranged in the orderin which the figures in the factor run. Concrete examples of such casesare shown in Figs. 5, 6and 8. In Fig. 5 the multiplication of thirty-twoand of eight hundred and seventy-six bya number containing three iiguresis represented. If the horizontal columns of the elements are arrangedin an order corresponding with the factors thirty-two and six hundredand seventy-eight and the oblique rows bounded by the diagonals formed,the following results are obtainedi In the case of the multiplication bythirty-two a is the unit; h -l- ZJ -ib2, tens; c c' -lc2 -lc3, hundreds;d -l- V+ d2, thousands, and f, tenthousands,while in the multiplicationof eight hundred and seven ty-six by a number containing three figures gis the unit; h h h2, the tens; fi-lz" -ic -I- 3 -l- 4, the hundreds; k-l- Zolla? 7e3 104, the thousands; Z-l- Zl- Z2, the tens of thousands,and m, the hundreds of thousands.

In Fig. 6 the in ultiplication of two hundred and fifty-eight by anumber containing three figures is represented. When the horizontalcolumns opposite the indices 2, 5, and 8 are arranged directly one underthe other, the following rows are formed: a, Z) -lb-}- b2,c-{-c}c2+c3c4, d-l-d-dz-l-ds-l-df, f+f'+f2, and

In Fig. 8 the multiplication of a number containing four figures byninety-seven thousand five hundred and thirty-one is represented-that isto say, by a number in which the figures run in an order opposite tothat of the natural numerical order, and thus form aconstantly-decreasing arithmetical series. Assuming the horizontalcolumn arranged in a line with the index 9 to be arranged above andbelow in accordance with the order of the columns 7, 5, 3, and 1, thefigures of the oblique rows are obtained, as shown in Fig. 8, byidentical lettering.

Finally, by means of Fig. 4 the case is represented in which one of thefactors-such, for example, as four hundred and forty-fourconsists ofseveral identical figures. In this instance the result is obtained bythe addition of three identical columns. In the foregoing case thefollowing result is obtained (see the horizontal column opposite theindex 4 a, unit; a-l-b-l-b,tens; a-|-Z2-{-b'-}clc', hundreds; h -lb' -lc-lc' -ld -ld,thousands; c -lc -id -l- CZ -lc -le, tens of thousands; d-ld -le -lc -l-f-l-f, hundreds of thousands; e -le -l-f-l-f' -lg', tensof millions, and g hundreds of millions. In orderto check this rule, themultiplication two hundred and twenty-two by eight hundred andthirty-six thousand five hundred and seventeen may bc effected by it..

From the above examples it will be seen that according as the figuresof' one of the factors assume a diderent position upon the index-bar,either in reversed numerical order separated one from the other by oneor more numbers in reversed numerical order and separated, ctc., theconnected numbers must be sought by various but regular transitions.;For the purpose of gaining experience in these transitions various formsor patterns may be employed which are cut in different places in such amanner that only the figures required-that is to say, the numbersforming an oblique row-are visible. Diderent patterns of coursecorrespond to different transitions. A pattern of this kind isrepresented in Fig. 7, which is suitable for effecting themultiplication ninety-seven thousand five hundred and thirty-one by onehundred and twenty-three million four hundred and fifty-six thousandseven hundred and eightynine, which represents tens of millions. Thevarious groups of numbers are rendered visible by the stepwisedisplacement of the pattern in a lateral direction. In order to renderthe manipulation of the pattern more easy, the bars, as shown in Figs. 7and 8, are laid between two parallel rails O, over which the pattern maybe laterally displaced.

In Fig. 8the rails are arranged in a box D, Y

thereby enabling the whole device to be conveniently carried or stored.

In order to be able to adjust the patterns te the various columns in thedirection of their height also, they are arranged in frames in such amanner that they may be slid up and IOC tof'

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down. Fig. 9 is a perspective view of such a frame. The frame E itselfis capable of being displaced along lthe rails C, while the pattern maybe displaced in the direction of its height beneath the members E E ofthe frame. As already stated, however, the use of these patterns is soonrendered unnecessary by practice so much the more that the coloring, redor otherwise, of the triangular spaces beneath the diagonals enables theoblique rows to be readily located and aords a restingpoint for the eyewhen looking for connected numbers.

What I claim, and desire to secure by Letters Patent of the UnitedStates, is-

A system of calculating-bars, consisting of an index-bar upon which the{igures l to 9 are inscribed in squares or divisions in numerical order,in combination with calcu lating-bars carrying at their respective headsthe figures 0 to 9 and below them in squares or divisions the multiplesof the respective head figures, whereby the product of a number on theindex-bar by the head numbers on the calculating-bars may be caused tolie in a horizontal row by placing the bars involved, side by side,substantially as described.

In testimony whereof I have hereunto -set my hand in the presence gf twowitnesses. ARPAD HORVATH. Witnesses:

GENSEN RTY, BAIEs LARso.

